Download isosceles trapezoid

isosceles trapezoid∗
Wkbj79†
2013-03-21 23:06:44
An isosceles trapezoid is a trapezoid whose legs are congruent and that has
two congruent angles such that their common side is a base of the trapezoid.
Thus, in an isosceles trapezoid, any two angles whose common side is a base of
the trapezoid are congruent.
In Euclidean geometry, the convention is to state the definition of an isosceles trapezoid without the condition that the legs are congruent, as this fact can
be proven in Euclidean geometry from the other requirements. For other geometries, such as hyperbolic geometry and spherical geometry, the condition that
the legs are congruent is essential for the definition of an isosceles trapezoid, as
the other requirements do not imply that the legs are congruent.
The common perpendicular bisector to the bases of an isosceles trapezoid
always divides the quadrilateral into two congruent right trapezoids. In other
words, every isosceles trapezoid is symmetric about the common perpendicular
to its bases.
Below is a picture of an isosceles trapezoid. The common perpendicular to
its bases is drawn in cyan.
In some dialects of English (e.g. British English), this figure is referred to as
an isosceles trapezium. Because of the modifier “isosceles”, no confusion should
arise with this usage.
All rectangles are isosceles trapezoids (unless the restricted definition of
trapezoid is used, see the entry on trapezoid for more details). Note that,
in Euclidean geometry, if a parallelogram is an isosceles trapezoid, then it must
be a rectangle.
∗ hIsoscelesTrapezoidi created: h2013-03-21i by: hWkbj79i version: h39519i Privacy
setting: h1i hDefinitioni h51-00i
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In Euclidean geometry, in a circle, the endpoints of two parallel chords are
the vertices of an isosceles trapezoid. Conversely, one may use four suitable
points on a circle for obtaining parallel chords (and thus parallel lines).
A right isosceles trapezoid is a trapezoid that is simultaneously a right trapezoid and an isosceles trapezoid. In Euclidean geometry, such trapezoids are
automatically rectangles. In hyperbolic geometry, such trapezoids are automatically Saccheri quadrilaterals. Thus, the phrase “right isosceles trapezoid”
occurs rarely.
A 3-sides-equal trapezoid is an isosceles trapezoid having at least three congruent sides. Below is a picture of a 3-sides-equal trapezoid.
In some dialects of English (e.g. British English), this figure is referred to as
a 3-sides-equal trapezium. Because of the modifier “3-sides-equal”, no confusion
should arise with this usage.
A rare but convenient alternative name for a 3-sides-equal trapezoid is a
trisosceles trapezoid ; the corresponding name trisosceles trapezium does not
seem to be in current usage.
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